盲信号分离算法分析与应用研究
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摘要
盲信号分离是信号处理领域非常重要的研究课题,在无线通讯、语音识别、信号加密、特征提取、信号抗干扰、遥感图像解译以及生物医学信号处理等领域具有广泛的应用前景,因而受到了越来越多学者的关注。尽管盲分离领域的发展很快,不过仍然存在如下问题:怎样分离相关源信号?如何处理大规模或者实时数据集?怎样处理欠定盲分离问题,特别是源信号数目未知的情况下怎样估计源的数目并分离源信号?如何使盲分离技术走向实际应用领域等等。本文从如下几方面继续探讨了盲分离问题:
首先,系统研究了基于非负矩阵分解(nonnegative matrix factorization,NMF)的盲分离方法。根据观测信号所体现出来的几何特征,在经典的NMF中添加了关于混叠矩阵体积的惩罚项。进而探讨了源信号的可分性条件,并分析了该条件与源信号稀疏特征之间的关系。同时,通过采用基于自然梯度的优化算法,使得传统的交替最小二乘乘法更新规则仍然适用于求解基于体积约束的NMF模型。该约束NMF方法特别适合处理相关信号的盲分离,同时由于采用了体积约束,不仅增强了基于NMF的盲分离方法的可辨识性,而且降低了对源信号的稀疏性要求。
其次,对大规模数据集或者实时数据集,论文介绍了增量或在线盲分离算法,特别推导了基于增量非负矩阵分解的在线盲分离方法。通过采用充分使用每个样本的“平均遗忘”学习手段,该方法既保障了学习的统计效率,又降低了计算消耗。由于在每次迭代时,消耗非常小,因而适合于处理在线盲分离问题。
然后,分析了稀疏信号的欠定盲分离问题。介绍了两类分离方法:1)二步法,即先通过具有优越分类性能的支持向量机方法来估计混叠矩阵,然后采用线性规划方法来恢复源信号,其中在估计混叠矩阵时采用定向非循环图方法将传统的二分类支持向量机推广到了多分类;2)同步法,采用基于约束自然梯度的交替更新优化算法,可以同时估计混叠矩阵和源信号。与传统采用近似梯度的方法不同,本文从理论上严格推导了学习混叠矩阵的实际梯度,相应的学习结果明显优于近似梯度方法。
此外,将盲分离策略用于语音和图像加密领域,提出了新型语音图像密码系统。具体介绍了该类密码系统的结构,包括预处理、加密、解密、重构等,并分析了其在几种常见攻击下的安全性。与传统的密码系统相比,该类系统具有结构简单,安全性更高、密码使用更加方便等特点。
最后,还将盲分离技术用于多光谱/超光谱遥感图像解译或谱解混。论文提出了基于高阶统计量的信号稀疏性新度量,其具有一定的物理含义,且便于优化。根据该度量,介绍了基于盲分离/稀疏非负矩阵分解的谱解混算法,可以同时估计端元和丰度。通过对人工合成数据集以及真实数据集的测试,表明了该方法在收敛性、对噪声的敏感性等方面优于传统的方法,特别适合处理稀疏端元,同时对稀疏度不够高的端元也具有很强的鲁棒性。
Blind source separation (BSS) is a hot topic in signal processing. It attracts more and more attentions because of its widely applications in wireless communication, speech identification, signal encryption, feature extraction, signal anti-interference, remote sensing image interpretation, and biomedical signal processing. The study about BSS develops very fast, but there still exist some problems, such as how to separate the dependent sources? How to solve large-scale or real time dataset? How to solve the underdetermined mixed model, especially when the source number is unknown? How to use BSS technology practically? This thesis exploits BSS problems from the following facts:
First, study the BSS method based on nonnegative matrix factorization (NMF) systematically. According to the geometrical feature of the observations, a volume constraint is added to the traditional NMF model. The separability conditions are proposed. And the relation between these conditions and the sparseness features are discussed. Also, a natural gradient based algorithm is utilized, such that the traditional alternative least square multiplication updating rule can solve the constrained NMF model. The proposed constrained NMF method is particularly suitable for the separation of dependent sources. Also, due to the volume constraint, the identifiability of NMF based method is enhanced and the requirement of sparseness to sources is reduced.
Second, online or incremental BSS algorithms are introduced for real-time or large-scale dataset, where the incremental NMF algorithm is mainly derived. Using an amnesic average method which allows full use of every sample, it realizes the statistical efficiency for learning and reduces the computational cost. As the cost is low at each iteration, the proposed method is particularly suitable for solving online BSS problem.
Then, the underdetermined BSS problem for sparse sources is analyzed. Two kinds of separation methods are introduced: 1) two-stage-method, i.e., estimating the mixing matrix using support vector machine (SVM) which has powerful performance for classification firstly, then recovering the sources by solving the linear program problems. For the estimation of the mixing matrix, the traditional two-classifying SVM is extended to multi-classifying by directed acyclic graph method. 2) one-stage-method, i.e., estimating the mixing matrix and the sources simultaneously using constrained natural gradient based alternative updating method. In stead of traditional method for learning the mixing matrix using approximate gradient, a strict natural gradient is derived in the proposed method. As a result, it has a much better performance.
Furthermore, the BSS scheme is used for speech and image encryption, and a new type cryptosystem is proposed. The structure is analyzed in detail, including preprocessing, encryption, decryption, reconstruction. The corresponding security under normal attacks is also analyzed. Compared with the state-of-the-art, the proposed cryptosystems have the following advantages: the structure is simpler, the usage of the cipher is more convenient, and the security is higher.
At last, the BSS scheme is used for remote sensing image interpretation or spectral unmixing. A novel measure of sparseness using higher order statistics of signals is proposed. It features the physical significance and is convenient to be optimized. Based on this measure, a sparse NMF/BSS algorithm is proposed for solving SU, where the endmembers and abundances are simultaneously estimated. Simulations based on synthetic mixtures and real images show that the proposed method outperforms the state-of-the-art methods, including the convergence, sensitivities to the noise, etc. It is particularly suitable for processing sparse endmembers, but also robust to process the endmembers which are not sparse enough.
首先,系统研究了基于非负矩阵分解(nonnegative matrix factorization,NMF)的盲分离方法。根据观测信号所体现出来的几何特征,在经典的NMF中添加了关于混叠矩阵体积的惩罚项。进而探讨了源信号的可分性条件,并分析了该条件与源信号稀疏特征之间的关系。同时,通过采用基于自然梯度的优化算法,使得传统的交替最小二乘乘法更新规则仍然适用于求解基于体积约束的NMF模型。该约束NMF方法特别适合处理相关信号的盲分离,同时由于采用了体积约束,不仅增强了基于NMF的盲分离方法的可辨识性,而且降低了对源信号的稀疏性要求。
其次,对大规模数据集或者实时数据集,论文介绍了增量或在线盲分离算法,特别推导了基于增量非负矩阵分解的在线盲分离方法。通过采用充分使用每个样本的“平均遗忘”学习手段,该方法既保障了学习的统计效率,又降低了计算消耗。由于在每次迭代时,消耗非常小,因而适合于处理在线盲分离问题。
然后,分析了稀疏信号的欠定盲分离问题。介绍了两类分离方法:1)二步法,即先通过具有优越分类性能的支持向量机方法来估计混叠矩阵,然后采用线性规划方法来恢复源信号,其中在估计混叠矩阵时采用定向非循环图方法将传统的二分类支持向量机推广到了多分类;2)同步法,采用基于约束自然梯度的交替更新优化算法,可以同时估计混叠矩阵和源信号。与传统采用近似梯度的方法不同,本文从理论上严格推导了学习混叠矩阵的实际梯度,相应的学习结果明显优于近似梯度方法。
此外,将盲分离策略用于语音和图像加密领域,提出了新型语音图像密码系统。具体介绍了该类密码系统的结构,包括预处理、加密、解密、重构等,并分析了其在几种常见攻击下的安全性。与传统的密码系统相比,该类系统具有结构简单,安全性更高、密码使用更加方便等特点。
最后,还将盲分离技术用于多光谱/超光谱遥感图像解译或谱解混。论文提出了基于高阶统计量的信号稀疏性新度量,其具有一定的物理含义,且便于优化。根据该度量,介绍了基于盲分离/稀疏非负矩阵分解的谱解混算法,可以同时估计端元和丰度。通过对人工合成数据集以及真实数据集的测试,表明了该方法在收敛性、对噪声的敏感性等方面优于传统的方法,特别适合处理稀疏端元,同时对稀疏度不够高的端元也具有很强的鲁棒性。
Blind source separation (BSS) is a hot topic in signal processing. It attracts more and more attentions because of its widely applications in wireless communication, speech identification, signal encryption, feature extraction, signal anti-interference, remote sensing image interpretation, and biomedical signal processing. The study about BSS develops very fast, but there still exist some problems, such as how to separate the dependent sources? How to solve large-scale or real time dataset? How to solve the underdetermined mixed model, especially when the source number is unknown? How to use BSS technology practically? This thesis exploits BSS problems from the following facts:
First, study the BSS method based on nonnegative matrix factorization (NMF) systematically. According to the geometrical feature of the observations, a volume constraint is added to the traditional NMF model. The separability conditions are proposed. And the relation between these conditions and the sparseness features are discussed. Also, a natural gradient based algorithm is utilized, such that the traditional alternative least square multiplication updating rule can solve the constrained NMF model. The proposed constrained NMF method is particularly suitable for the separation of dependent sources. Also, due to the volume constraint, the identifiability of NMF based method is enhanced and the requirement of sparseness to sources is reduced.
Second, online or incremental BSS algorithms are introduced for real-time or large-scale dataset, where the incremental NMF algorithm is mainly derived. Using an amnesic average method which allows full use of every sample, it realizes the statistical efficiency for learning and reduces the computational cost. As the cost is low at each iteration, the proposed method is particularly suitable for solving online BSS problem.
Then, the underdetermined BSS problem for sparse sources is analyzed. Two kinds of separation methods are introduced: 1) two-stage-method, i.e., estimating the mixing matrix using support vector machine (SVM) which has powerful performance for classification firstly, then recovering the sources by solving the linear program problems. For the estimation of the mixing matrix, the traditional two-classifying SVM is extended to multi-classifying by directed acyclic graph method. 2) one-stage-method, i.e., estimating the mixing matrix and the sources simultaneously using constrained natural gradient based alternative updating method. In stead of traditional method for learning the mixing matrix using approximate gradient, a strict natural gradient is derived in the proposed method. As a result, it has a much better performance.
Furthermore, the BSS scheme is used for speech and image encryption, and a new type cryptosystem is proposed. The structure is analyzed in detail, including preprocessing, encryption, decryption, reconstruction. The corresponding security under normal attacks is also analyzed. Compared with the state-of-the-art, the proposed cryptosystems have the following advantages: the structure is simpler, the usage of the cipher is more convenient, and the security is higher.
At last, the BSS scheme is used for remote sensing image interpretation or spectral unmixing. A novel measure of sparseness using higher order statistics of signals is proposed. It features the physical significance and is convenient to be optimized. Based on this measure, a sparse NMF/BSS algorithm is proposed for solving SU, where the endmembers and abundances are simultaneously estimated. Simulations based on synthetic mixtures and real images show that the proposed method outperforms the state-of-the-art methods, including the convergence, sensitivities to the noise, etc. It is particularly suitable for processing sparse endmembers, but also robust to process the endmembers which are not sparse enough.
引文
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